Method and apparatus for determining a process model that models the impact of CAR/PEB on the resist profile

ABSTRACT

An embodiment provides systems and techniques for determining a process model. During operation, the system may receive a first optical model which models a first optical system of a photolithography process. Next, the system may use the first optical model to determine a second optical model that models a second latent image that is formed by the first optical system at a second distance. The system may also use the first optical model to determine a third optical model that models a third latent image that is formed by the first optical system at a third distance. Next, the system may receive process data which is obtained by subjecting a test layout to the photolithography process. The system may then determine a process model using the first optical model, the second optical model, the third optical model, the test layout, and the process data.

RELATED APPLICATION

This application is a continuation-in-part of, and hereby claimspriority under 35 U.S.C. § 120 to, U.S. patent application Ser. No.11/443,715, which was filed on 31 May 2006 by the same inventors as theinstant application, and which was entitled “METHOD AND APPARATUS FORDETERMINING AN ACCURATE PHOTOLITHOGRAPHY PROCESS MODEL,” and which ishereby incorporated by reference to describe a process for determiningan optical process model.

BACKGROUND

1. Field of the Invention

The present invention relates to integrated circuit design andfabrication. More specifically, the present invention relates to amethod and an apparatus to determine a photolithography process modelthat models the impact of CAR/PEB (Chemically Amplified Resist PostExposure Bake) on the resist profile.

2. Related Art

Rapid advances in computing technology have made it possible to performtrillions of computational operations each second on data sets that aresometimes as large as trillions of bytes. These advances can beattributed to the dramatic improvements in semiconductor manufacturingtechnologies which have made it possible to integrate tens of millionsof devices onto a single chip.

As semiconductor design enters the deep submicron era, process modelaccuracy is becoming increasingly important. Inaccuracies in the processmodel negatively affect the efficacy of downstream applications. Forexample, inaccuracies in the photolithography process model can reducethe efficacy of optical proximity correction (OPC). Hence, it isdesirable to improve process model accuracy.

SUMMARY

One embodiment of the present invention provides systems and techniquesfor determining an accurate process model. A process model usually needsto be very fast and accurate, and hence, insignificant physical effectsare often ignored during modeling to improve simulation performance.However, as semiconductor integration densities continue to increase atexponential rates, a number of physical effects that were ignored in thepast can no longer be ignored.

One factor that is typically ignored in conventional techniques, butwhich is becoming increasingly significant, is the printed resistprofile in the Z direction. The printed resist profile in the Zdirection can have a slope due to the diffusion of acids in thephotoresist and/or due to the fact that the printed features are belowthe exposure resolution limit. The characteristics of the printed resistprofile in the Z direction can affect the behavior of subsequentprocesses, such as etch.

An embodiment models the effect of CAR/PEB on the printed resist profilein the Z direction. Specifically, the embodiment can model a defocusedaerial image at a distance that is different from the best focusdistance to account for the aerial image signal difference betweenphotoresist depths, and diffuses the aerial image using a Gaussiankernel to account for the diffusion length difference between the Zdirection and the X/Y directions.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention.

FIG. 2 illustrates a typical optical system in accordance with anembodiment of the present invention.

FIG. 3 presents a flow chart that illustrates a process for determininga process model that models the impact of CAR/PEB on the resist profileand/or the impact of the gradient-magnitude of the aerial imageintensity in accordance with an embodiment of the present invention.

FIG. 4 illustrates how latent images can be formed at differentdistances in accordance with an embodiment of the present invention.

FIGS. 5A, 5B, and 5C illustrate how latent images can be formed on aplane by varying the focal length in accordance with an embodiment ofthe present invention.

FIG. 6 illustrates how a system can determine and use a process model inaccordance with an embodiment of the present invention.

FIG. 7 illustrates how a process model can be stored in acomputer-readable storage medium in accordance with an embodiment of thepresent invention.

FIG. 8 illustrates a resist profile in the Z direction in accordancewith an embodiment of the present invention.

DETAILED DESCRIPTION Integrated Circuit (IC) Design Flow

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention.

The process starts with the conception of the product idea (step 100)which is realized using an EDA software design process (step 110). Whenthe design is finalized, it can be taped-out (event 140). After tapeout, the fabrication process (step 150) and packaging and assemblyprocesses (step 160) are performed which ultimately result in finishedchips (result 170).

The EDA software design process (step 110), in turn, comprises steps112-130, which are described below. Note that the design flowdescription is for illustration purposes only. This description is notmeant to limit the present invention. For example, an actual integratedcircuit design may require the designer to perform the design steps in adifferent sequence than the sequence described below. The followingdiscussion provides further details of the steps in the design process.

System design (step 112): In this step, the designers describe thefunctionality that they want to implement. They can also perform what-ifplanning to refine functionality, check costs, etc. Hardware-softwarearchitecture partitioning can occur at this stage. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude Model Architect, Saber®, System Studio, and DesignWare®products.

Logic design and functional verification (step 114): At this stage, theVHDL or Verilog code for modules in the system is written and the designis checked for functional accuracy. More specifically, the design ischecked to ensure that it produces the correct outputs. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude VCS®, Vera®, DesignWare®, Magellan™, Formality®, ESP and Leda®products.

Synthesis and design for test (step 116): Here, the VHDL/Verilog istranslated to a netlist. The netlist can be optimized for the targettechnology. Additionally, tests can be designed and implemented to checkthe finished chips. Exemplary EDA software products from Synopsys, Inc.that can be used at this step include Design Compiler®, PhysicalCompiler®, Test Compiler, Power Compiler™, FPGA Compiler, TetraMAX®, andDesignWare® products.

Netlist verification (step 118): At this step, the netlist is checkedfor compliance with timing constraints and for correspondence with theVHDL/Verilog source code. Exemplary EDA software products from Synopsys,Inc. that can be used at this step include Formality®, PrimeTime®, andVCS® products.

Design planning (step 120): Here, an overall floorplan for the chip isconstructed and analyzed for timing and top-level routing. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude Astro™ and IC Compiler products.

Physical implementation (step 122): The placement (positioning ofcircuit elements) and routing (connection of the same) occurs at thisstep. Exemplary EDA software products from Synopsys, Inc. that can beused at this step include the Astro™ and IC Compiler products.

Analysis and extraction (step 124): At this step, the circuit functionis verified at a transistor level, this in turn permits what-ifrefinement. Exemplary EDA software products from Synopsys, Inc. that canbe used at this step include AstroRail™, PrimeRail, PrimeTime®, andStar-RCXT™ products.

Physical verification (step 126): In this step, the design is checked toensure correctness for manufacturing, electrical issues, lithographicissues, and circuitry. Exemplary EDA software products from Synopsys,Inc. that can be used at this step include the Hercules™ product.

Resolution enhancement (step 128): This step involves geometricmanipulations of the layout to improve manufacturability of the design.Exemplary EDA software products from Synopsys, Inc. that can be used atthis step include Proteus/Progen, ProteusAF, and PSMGen products.

Mask data preparation (step 130): This step provides the “tape-out” datafor production of masks to produce finished chips. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude the CATS® family of products.

Embodiments of the present invention can be used during one or more ofthe above-described steps. Specifically, one embodiment of the presentinvention can be used during the resolution enhancement step 128.

Process Model

A process model models the behavior of one or more semiconductormanufacturing processes which typically involve complex physical andchemical interactions. A process model is usually determined by fittingkernel coefficients to empirical data. The empirical data is usuallygenerated by applying the semiconductor manufacturing processes that arebeing modeled to one or more test layouts. For example, aphotolithography process can be used to print a test layout on a wafer.Next, the empirical data can be obtained by measuring the criticaldimensions (CD) of features on the resulting wafer before and/or afterthe etch process. The process model can then be fit to the empiricaldata to determine a process model that models the photolithographyprocess.

Once a process model is determined, it can be used in a number ofapplications during the design and manufacture of a semiconductor chip.For example, process models are typically used to support OpticalProximity Correction (OPC) and Resolution Enhancement Techniques (RET).These models can allow full-chip database manipulation in reasonabletimeframes during the tapeout flow.

A process model can include functions or kernels that are associatedwith parameters and/or coefficients which are statistically fit toempirical data. A function or a kernel can be any mathematicalexpression.

For example, a process model may be represented as

${\sum\limits_{i}\left( {C_{i} \cdot K_{i}} \right)},$

where K_(i) is a modeling function or kernel, and C_(i) is a coefficientwhich is associated with K_(i). The empirical data may include values ofa desired property, e.g., the CD, at different locations in the layout.Once the process model is fit to the empirical data, it can then be usedto predict the value of the desired property for other layouts.

Ideally, we may want to determine coefficient values which will causethe predicted data to exactly match the empirical data. However, anexact fit is usually not possible, and even if it is possible, it maynot be desirable because the resulting process model may not interpolateand/or extrapolate properly. Hence, statistical fitting techniques aretypically used to determine the parameters and/or coefficients so thatthe error between the empirical data and the predicted data isminimized. In one embodiment, the system can use a least-squares fittingtechnique to determine the parameter and/or coefficient values.

A process model is considered to be robust if it interpolates andextrapolates well, i.e., if the process model generates accurate resultswhen it is applied to layouts that are different from the layouts thatwere used during the fitting process. In general, the fewer modelingfunctions or kernels that a process model uses, the more robust it is.However, using fewer kernels may decrease the process model's accuracy.Hence, there is usually a tradeoff between the robustness and theaccuracy of a process model.

Photolithography Process Model

The optical model in a photolithography process model is usually basedon the Hopkins model which uses the principles of optics to model thebehavior of partially coherent optical systems.

FIG. 2 illustrates a typical optical system in accordance with anembodiment of the present invention.

Radiation from source 202 can be collimated by a condenser 204. Thecollimated light can then pass through mask 206, aperture 208, lens body210, and form an image on a wafer 212.

Specifically, the Hopkins model can be described using the expression:

I(x,y)=∫∫∫∫J(x′,y′;x″,y″)

L(x,y;x′,y′)

L*(x,y;x″,y″)dx′dy′dx″dy″,

where, I(x, y) is the optical intensity at point (x, y) on the wafer,L(x,y;x′,y′) is a lumped model of the light source and the mask, L* isthe complex conjugate of L, and J(x′,y′;x″,y″) models the incoherencebetween two points of light on the mask. The lumped model (L)essentially treats the mask as an array of light sources. In particular,L(x,y;x′,y′) models point (x′,y′) on the mask as a point source, andJ(x′,y′;x″,y″) models the incoherence between the light emanating frompoints (x′,y′) and (x″,y″) on the mask. The lumped model (L) can berepresented as a convolution between the mask and the source. Forexample, the lumped model can be represented using a mask model and asource model as follows:

L(x,y;x′,y′)=M(x′,y′)

K(x,y;x′,y′),

where M(x′,y′) models the mask and K(x,y;x′,y′) models the source.

The Hopkins model can be used to determine a 4-D (four dimensional)matrix called the Transmission Cross Coefficient (TCC) matrix whichmodels the optical system. The TCC matrix can then be represented usinga set of orthogonal 2-D (two dimensional) kernels. Specifically, the setof orthogonal kernels can be determined using the eigenfunctions of theTCC matrix. The features on the wafer can be determined by convolvingthe set of 2-D kernels with the mask. General information onphotolithography and process modeling can be found in Alfred Kwok-KitWong, Optical Imaging in Projection Microlithography, SPIE-InternationalSociety for Optical Engine, 2005, and Grant R. Fowles, Introduction toModern Optics, 2^(nd) Edition, Dover Publications, 1989.

In one embodiment, the system uses Zernike polynomials, which are a setof orthogonal functions, to represent the optical system. Zernikepolynomials are made up of terms that are of the same form as the typesof aberrations often observed in optical systems. For example, oneZernike polynomial may be associated with defocus, while another may beassociated with tilt, etc. Zernike polynomials are usually representedin polar coordinates. Specifically, the optical system can berepresented using the expression

${\sum\limits_{i}\left( {C_{i} \cdot Z_{i}} \right)},$

where Z_(i) is a Zernike polynomial and C_(i) is an optical coefficientwhich is associated with Z_(i).

Chemically Amplified Resist Post Exposure Bake Effects

A process model usually needs to be very fast and accurate. As such,“small” physical effects are often ignored during modeling to increasesimulation speed. However, the physical effects that are “small” at oneprocess node may become significant at another process node. One sucheffect that was often ignored in the past, but which is becomingincreasingly significant, is the Z direction diffusion of acids in thephotoresist. At the 45 nm process node this physical effect may causeprocess model errors of 5% or greater, and hence this effect needs to bemodeled in the process model without sacrificing computationalperformance.

In addition to accuracy and performance, the Time To Accurate Model(TTAM) is another important property of a process model. The TTAM is theamount of time it takes to determine an acceptably accurate processmodel by fitting an uncalibrated process model to process data.Obviously, a low TTAM value is desirable.

Chemicaly Amplified Resist Post Exposure Bake (CAR/PEB) effects havegrown more significant at the 45 nm and 32 nm process nodes for OpticalProximity Correction (OPC) model calibration. In conventionalapproaches, CAR/PEB effects are modeled using reaction diffusionkinetics of chemically amplified resist during post exposure bakeprocesses. However, these conventional approaches are impractical forOPC modeling applications because they are too slow since they requirethe system to solve nonlinear partial differential equations. Moreover,conventional approaches do not accurately model the printed resistprofile in the Z direction because they use the aerial image intensityat a single latitude (or distance) or they use the average of the aerialimage intensities over multiple latitudes.

An OPC model needs to account for CAR/PEB effects because the modelneeds to simulate the signal change from a measured line-widthdifference. For example, the resist profiles in the Z direction can bedifferent for line/space patterns and line-ends. This difference in theresist profile can significantly affect the behavior of subsequentprocesses, e.g., the resist profile can affect the amount of etch bias.Hence, the model needs to simulate the aerial image signal difference(which corresponds to the diffusion length) between the Z direction andthe X/Y directions.

FIG. 8 illustrates a resist profile in the Z direction in accordancewith an embodiment of the present invention.

The resist pattern shown in FIG. 8 includes printed lines 802 and 804.Printed lines 802 and 804 are both part of a line and space pattern, butprinted line 804 includes an isolated extension. Resist profile 806represents the profile of region 816 in the Z direction. Resist profile808 represents the profile of region 818 in the Z direction. Note thatresist profile 806 is steeper than resist profile 808. One reason forthe difference in the slopes of the resist profiles is the fact that thegradient-magnitude of the aerial image intensity in region 806 isgreater than the gradient-magnitude of the aerial image intensity inregion 808.

Conventional models model the aerial image at a fixed depth, e.g.,nominal depth 812. Hence, conventional techniques cannot accuratelymodel the difference between the resist profiles of isolated features(e.g., extension of printed line 804) and dense features (e.g., printedline 802). One embodiment of the present invention uses the aerial imageat multiple latitudes (or depths) to model the resist profiles ofisolated and dense features. For example, an embodiment can model theaerial image at depth 810 and 814. Next, the embodiment can use theseaerial images to generate a photolithography process model thataccurately models the effect of CAR/PEB on the resist profile and/or theeffect of the gradient-magnitude of the aerial image on the resistprofile.

One embodiment of the present invention provides systems and techniquesfor determining a process model that accurately models CAR/PEB effectswithout sacrificing runtime performance. An embodiment models adefocused aerial image at a distance with same defocus or differentdefocus value that can be different from the best focus distance toaccount for the aerial image signal difference between photoresistdepths. Next, the embodiment diffuses the aerial image using a Gaussiankernel to account for the diffusion length difference between the Zdirection and the X/Y directions.

A Photolithography Process Model that Models CAR/PEB Effects

FIG. 3 presents a flow chart that illustrates a process for determininga process model that models the impact of CAR/PEB on the resist profileand/or the impact of the gradient-magnitude of the aerial imageintensity in accordance with an embodiment of the present invention.

The process can begin by receiving a first optical model (stage 302)which models a first optical system of a photolithography process.

Next, the system can use the first optical model to determine a secondoptical model (stage 304). In one embodiment, the second optical modelcan model a second latent image that is formed by the first opticalsystem at a second distance that is different from the first opticalsystem's best focus distance. In another embodiment, the second opticalmodel can model a second latent image that is formed by a second opticalsystem at the first optical system's best focus distance. In yet anotherembodiment, the second optical model can model a second latent imagethat is formed by a second optical system at a second distance that isdifferent from the first optical system's best focus distance.

The system can then use the first optical model to determine a thirdoptical model (stage 306). In one embodiment, the third optical modelcan model a third latent image that is formed by the first opticalsystem at a third distance that is different from the first opticalsystem's best focus distance. In another embodiment, the third opticalmodel can model a third latent image that is formed by a third opticalsystem at the first optical system's best focus distance. In yet anotherembodiment, the third optical model can model a third latent image thatis formed by a third optical system at a third distance that isdifferent from the first optical system's best focus distance.

Note that the second distance, the third distance, and the first opticalsystem's best focus distance can be different from one another. Further,note that the chemically amplified resist post exposure bake effects canbe modeled using the second optical model and the third optical model.

FIG. 4 illustrates how latent images can be formed at differentdistances in accordance with an embodiment of the present invention.

Lens 402 is part of an optical system of a photolithography process. Thephotolithography process uses lens 402 to image a mask layout onphotoresist layer 404. (Note that photoresist layer 404 is not drawn toscale. The photoresist layer is typically very thin; however, it hasbeen magnified in FIG. 404 for illustration purposes.)

The best focus distance of an optical system is defined by the locationof the plane where we ideally want the mask layout to image. In FIG. 4,plane 408 is located at lens 402's best focus distance. Planes 406 and410 are located at distances that are different from lens 402's bestfocus distance.

The second and third optical models model the latent images at distancesthat are different from the best focus distance. For example, the secondoptical model can model the latent image at plane 406, and the thirdoptical model can model the latent image at plane 408.

FIGS. 5A, 5B, and 5C illustrate how latent images can be formed on aplane by varying the focal length in accordance with an embodiment ofthe present invention.

In FIG. 5A, lens 502 is part of an optical system that is used by aphotolithography process to generate an image on photoresist layer 504.Plane 508 is located at the best focus distance of lens 402 (shown inFIG. 4). Lens 502's focal length, however, is different from lens 402'sfocal length. Specifically, plane 506 is lens 502's best focus distance.Hence, the image formed at plane 508 is defocused. In one embodiment,the second optical model models the latent image formed by the lens(e.g., lens 502) of a second optical system at a plane (e.g., plane 508)that is located at the first optical system's best focus distance.

Similarly, in FIG. 5B, lens 552 is part of an optical system that isused by a photolithography process to generate an image on photoresistlayer 554. Plane 558 is located at the best focus distance of lens 402(shown in FIG. 4). Lens 552's focal length, however, is different fromlens 402's focal length. Specifically, plane 556 is lens 552's bestfocus distance. Hence, the image formed at plane 558 is defocused. Inone embodiment, the third optical model models the latent image formedby the lens (e.g., lens 552) of a third optical system at a plane (e.g.,plane 558) that is located at the first optical system's best focusdistance.

Note that the optical system's focal distance and the location of theimage can be changed simultaneously. For example, in FIG. 5C, the thirdmodel can model the latent image formed by the lens (e.g., lens 552) ofa third optical system at a plane (e.g., plane 560) that is located at adistance that is different from the third optical system's best focusdistance.

The system can then determine a process model using the first opticalmodel, the second optical model, the third optical model, a test layout,and process data associated with the test layout. In one embodiment, thesystem can first determine an uncalibrated process model using the firstoptical model, the second optical model, and the third optical model.Next, the system can fit the uncalibrated process model using theprocess data.

Specifically, the system can convolve the second optical model with asecond Gaussian kernel to obtain a second diffused model (stage 308).

The system can also convolve the third optical model with a thirdGaussian kernel to obtain a third diffused model (stage 310).

Next, the system can receive process data (stage 312) which is obtainedby subjecting a test layout to the photolithography process.

The system can then determine an uncalibrated process model using thefirst optical model, the second diffused model, and the third diffusedmodel (stage 314). Note that the system doesn't have to use both thesecond diffused model and the third diffused model. Specifically, in oneembodiment, the system may determine an uncalibrated process model usingthe first model and the second model.

In one embodiment, the uncalibrated process model, I_(U), is expressedas:

I _(U) =C ₁ ·I ₁ +C ₂·(G ₂

I ₂)+C ₃·(G ₃

I ₃),  (1)

where, I₁, I₂, I₃ are the first, second, and third optical models,respectively, C₁, C₂, C₃ are the first, second, and third coefficients,respectively, and G₂, G₃ are the second and third Gaussian kernels,respectively.

Next, the system can determine a process model by fitting theuncalibrated process model to the process data (stage 316).

FIG. 6 illustrates how a system can determine and use a process model inaccordance with an embodiment of the present invention.

Computer system 602 comprises processor 604, memory 606, and storagedevice 608. Computer system 602 can be coupled to display 614, keyboard610, and pointing device 612. Storage device 608 can store applications616 and 618, and process model 620.

During operation, computer system 602 can load application 616 intomemory 606. Next, the system can use application 616 to determineprocess model 620. Application 616 can then store process model 620 onstorage device 608.

Note that the system can store a process model by storing the parametersand/or coefficients in a computer-readable storage medium. In oneembodiment, the system may store parameters, coefficients, kernelidentifiers, and information that associates the parameters andcoefficients with their respective kernel identifiers. A kernelidentifier can be a string that identifies a kernel, or it can be anexpression that represents the kernel.

Next, the system can load application 618 into memory 606. Application618 can then load process model 620 into memory 606, and use processmodel 620 to determine a proximity correction or to predict the shape ofa pattern on a photoresist layer.

FIG. 7 illustrates how a process model can be stored in acomputer-readable storage medium in accordance with an embodiment of thepresent invention.

User 702 may use computer 704 to determine a process model. Next, user702 may store the parameters, coefficients, kernel identifiers, andinformation that associates the parameters and coefficients to thekernel identifiers on computer 704's hard disk or a removablecomputer-readable storage medium. Alternatively, user 702 may store theprocess model on database 712 which is coupled to computer 704 vianetwork 710. User 706 may receive the process model from user 702 overnetwork 710. Alternatively, user 706 may retrieve the process model fromdatabase 712. User 706 can load the process model on computer 708 byreading the parameters, coefficients, kernel identifiers, and theinformation that associates the parameters and coefficients to thekernel identifiers.

CONCLUSION

The data structures and code described in this detailed description aretypically stored on a computer-readable storage medium, which may be anydevice or medium that can store code and/or data for use by a computersystem. This includes, but is not limited to, volatile memory,non-volatile memory, magnetic and optical storage devices such as diskdrives, magnetic tape, CDs (compact discs), DVDs (digital versatilediscs or digital video discs), or other media capable of storingcomputer readable media now known or later developed.

Furthermore, the foregoing descriptions of embodiments of the presentinvention have been presented only for purposes of illustration anddescription. They are not intended to be exhaustive or to limit thepresent invention to the forms disclosed. Accordingly, manymodifications and variations will be readily apparent to practitionersskilled in the art. Additionally, the above disclosure is not intendedto limit the present invention. The scope of the present invention isdefined by the appended claims.

1. A method for determining a process model, the method comprising:receiving a first optical model which models a first optical system of aphotolithography process; using the first optical model to determine asecond optical model that models a second latent image that is formed bythe first optical system at a second distance; using the first opticalmodel to determine a third optical model that models a third latentimage that is formed by the first optical system at a third distance;receiving process data which is obtained by subjecting a test layout tothe photolithography process; and determining a process model using thefirst optical model, the second optical model, the third optical model,the test layout, and the process data.
 2. The method of claim 1, whereinthe second distance, the third distance, and the first optical system'sbest focus distance are different from one another.
 3. The method ofclaim 1, wherein chemically amplified resist post exposure bake effectsare modeled using the second optical model and the third optical model.4. The method of claim 1, wherein determining the process modelincludes: determining an uncalibrated process model using the firstoptical model, the second optical model, and the third optical model;and fitting the uncalibrated process model using the process data. 5.The method of claim 4, wherein determining the uncalibrated processmodel includes: convolving the second optical model with a secondGaussian kernel to obtain a second diffused model; convolving the thirdoptical model with a third Gaussian kernel to obtain a third diffusedmodel; and determining the uncalibrated process model using the firstoptical model, the second diffused model, and the third diffused model.6. A computer-readable storage medium storing instructions that whenexecuted by a computer cause the computer to perform a method fordetermining a process model, the method comprising: receiving a firstoptical model which models a first optical system of a photolithographyprocess; using the first optical model to determine a second opticalmodel that models a second latent image that is formed by the firstoptical system at a second distance; using the first optical model todetermine a third optical model that models a third latent image that isformed by the first optical system at a third distance; receivingprocess data which is obtained by subjecting a test layout to thephotolithography process; and determining a process model using thefirst optical model, the second optical model, the third optical model,the test layout, and the process data.
 7. The computer-readable storagemedium of claim 6, wherein the second distance, the third distance, andthe first optical system's best focus distance are different from oneanother.
 8. The computer-readable storage medium of claim 6, whereinchemically amplified resist post exposure bake effects are modeled usingthe second optical model and the third optical model.
 9. Thecomputer-readable storage medium of claim 6, wherein determining theprocess model includes: determining an uncalibrated process model usingthe first optical model, the second optical model, and the third opticalmodel; and fitting the uncalibrated process model using the processdata.
 10. The computer-readable storage medium of claim 9, whereindetermining the uncalibrated process model includes: convolving thesecond optical model with a second Gaussian kernel to obtain a seconddiffused model; convolving the third optical model with a third Gaussiankernel to obtain a third diffused model; and determining theuncalibrated process model using the first optical model, the seconddiffused model, and the third diffused model.
 11. A method fordetermining a process model, the method comprising: receiving a firstoptical model which models a first optical system of a photolithographyprocess; using the first optical model to determine a second opticalmodel that models a second latent image that is formed by a secondoptical system at the first optical system's best focus distance; usingthe first optical model to determine a third optical model that models athird latent image that is formed by a third optical system at the firstoptical system's best focus distance; receiving process data which isobtained by subjecting a test layout to the photolithography process;and determining a process model using the first optical model, thesecond optical model, the third optical model, the test layout, and theprocess data.
 12. The method of claim 11, wherein the first opticalsystem's best focus distance, the second optical system's best focusdistance, and the third optical system's best focus distance aredifferent from one another.
 13. The method of claim 11, whereinchemically amplified resist post exposure bake effects are modeled usingthe second optical model and the third optical model.
 14. The method ofclaim 11, wherein determining the process model includes: determining anuncalibrated process model using the first optical model, the secondoptical model, and the third optical model; and fitting the uncalibratedprocess model using the process data.
 15. The method of claim 14,wherein determining the uncalibrated process model includes: convolvingthe second optical model with a second Gaussian kernel to obtain asecond diffused model; convolving the third optical model with a thirdGaussian kernel to obtain a third diffused model; and determining theuncalibrated process model using the first optical model, the seconddiffused model, and the third diffused model.
 16. A computer-readablestorage medium storing instructions that when executed by a computercause the computer to perform a method for determining a process model,the method comprising: receiving a first optical model which models afirst optical system of a photolithography process; using the firstoptical model to determine a second optical model that models a secondlatent image that is formed by a second optical system at the firstoptical system's best focus distance; using the first optical model todetermine a third optical model that models a third latent image that isformed by a third optical system at the first optical system's bestfocus distance; receiving process data which is obtained by subjecting atest layout to the photolithography process; and determining a processmodel using the first optical model, the second optical model, the thirdoptical model, the test layout, and the process data.
 17. Thecomputer-readable storage medium of claim 16, wherein the first opticalsystem's best focus distance, the second optical system's best focusdistance, and the third optical system's best focus distance aredifferent from one another.
 18. The computer-readable storage medium ofclaim 16, wherein chemically amplified resist post exposure bake effectsare modeled using the second optical model and the third optical model.19. The computer-readable storage medium of claim 16, whereindetermining the process model includes: determining an uncalibratedprocess model using the first optical model, the second optical model,and the third optical model; and fitting the uncalibrated process modelusing the process data.
 20. The computer-readable storage medium ofclaim 19, wherein determining the uncalibrated process model includes:convolving the second optical model with a second Gaussian kernel toobtain a second diffused model; convolving the third optical model witha third Gaussian kernel to obtain a third diffused model; anddetermining the uncalibrated process model using the first opticalmodel, the second diffused model, and the third diffused model.